Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay

We prove the existence of solutions for the neutral periodic integrodifferential equation with infinite delay x (t)=G(t,x(t),x(t\tau(t))+\frac{d}{dt}Q(t,x(t\tau(t))+\in_{\infty}}^t\Sigma_{j=1}^n\big(g_j(t,s)\big)f(x(s))ds A Krasnoselskii and Banach s fixed point theorems are employed in establishing our results.